How to Calculate the Tax Multiplier
The tax multiplier equals −MPC ÷ MPS; multiply it by the change in taxes to find the change in GDP. It is negative and smaller than the spending multiplier.
The Tax Multiplier formula
Calculator
Enter the MPC and the change in taxes to get the tax multiplier and the change in GDP it produces.
Fraction of each extra dollar of income that households spend. MPS = 1 minus this.
Negative for a tax cut, positive for a tax increase.
A $20B tax cut raises GDP by $60B, less than the $80B the same amount of direct government spending would deliver.
- MPS
- 0.25
- Change in GDP
- $60B
- Spending multiplier for comparison
- 4
MPS = 1 minus MPC. It is the denominator of both multipliers.
Government spending enters aggregate demand dollar for dollar in round one, so its multiplier is always larger by exactly 1.
How to calculate Tax Multiplier, step by step
- 1Find the MPC and MPS. MPC is the fraction of extra income spent; MPS = 1 − MPC.
- 2Compute the multiplier. Tax multiplier = −MPC ÷ MPS. The negative sign means taxes and GDP move in opposite directions.
- 3Apply it to the tax change. ΔGDP = tax multiplier × Δtaxes. A tax cut is a negative Δtaxes, so it raises GDP.
Worked example: Tax Multiplier
If MPC = 0.75, the tax multiplier = −0.75 ÷ 0.25 = −3. A $20B tax cut (Δtaxes = −$20B) changes GDP by −3 × (−20) = +$60B, versus +$80B if the government had spent $20B directly (multiplier 1 ÷ 0.25 = 4).
Why it is smaller, and negative
The negative sign is the easy half: a tax rise takes money out, so output moves the other way. The size is the part that gets missed.
A dollar of government purchases enters the economy in full, because the government spends all of it by definition. A dollar of tax cut lands in a household's pocket first, and the household spends only the MPC share of it. The rest is saved and leaks out immediately. So the tax change starts its chain one round late and at a smaller size.
That is exactly why the tax multiplier is the spending multiplier times MPC, with the sign flipped. At an MPC of 0.8 the spending multiplier is 5 and the tax multiplier is −4, and the ratio between them is 0.8, the MPC itself.
In numbers: $100 billion of purchases supports up to $500 billion of extra real GDP, while a $100 billion tax cut supports up to $400 billion.
The balanced budget result
Raise spending and taxes by the same amount and the two effects do not cancel. Adding the multipliers gives 5 + (−4) = 1, so a balanced $100 billion package still raises real GDP by about $100 billion.
The reason is the asymmetry above. The government spends its whole $100 billion; the households handing over $100 billion in tax cut their spending by only the MPC share of it, because they cover part of the tax bill out of saving. The difference is what is left over.
The balanced budget multiplier is 1 for any MPC, which is a satisfying result and a good check on your arithmetic: if your spending and tax multipliers do not add to 1, one of them is wrong.
Tax Multiplier questions
What is the tax multiplier formula?
Tax multiplier = -MPC ÷ (1 - MPC) = -MPC ÷ MPS. Multiply it by the change in taxes to get the change in GDP: ΔGDP = tax multiplier × Δtaxes. Example: MPC = 0.75 gives -0.75 ÷ 0.25 = -3.
Why is the tax multiplier weaker than the spending multiplier?
Government spending enters aggregate demand dollar-for-dollar in round one, but a tax cut first becomes disposable income and households save the MPS share, only the MPC share is spent initially.
What is the balanced budget multiplier?
If spending and taxes rise by the same amount, the effects net to a multiplier of 1: spending multiplier + tax multiplier = 1 ÷ MPS + (−MPC ÷ MPS) = 1. GDP rises by exactly the amount spent.
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